"I knowed a doctor by the name of Heck (Peck?)
Fell into the well and broke his god-dog neck
Served him right, he was in the wrong
He ought to tend the sick and let the wells alone."

Brewer's song appears to be a reworking of "Old Black Crow in the Hickory Nut Tree," recorded by the Allen Brothers on 11/22/1930 (Victor 23551). The melody is slightly different, but only slightly, and most of the Brewer lyrics are very similar to the Allens', though his version is shorter. His chorus sounds, melodically and lyrically, like a rewrite of the Allens':

"Now ain't that so?
I don't know, I don't know.
Certainly is a mystery
About an old black crow in a hickory nut tree."

There's a thread about the "Old Black Crow/Story the Crow Told Me" group of songs. thread.cfm?threadid=95777
See the first post in the thread for a link to the Honking Duck real audio copy of the Allen Brothers recording.

The verse about the peacock parallels one in Blind Blake's "Lowdown Loving Gal of Mine," recorded in 9/1928 on the Paramount label:

"When the rooster saw the eggs and they was red
He went across the road and knocked the peacock dead
I tried to do that to that ever loving gal of mine."